-30x^4+3x^2+5=0

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Solution for -30x^4+3x^2+5=0 equation: 


Simplifying
-30x4 + 3x2 + 5 = 0

Reorder the terms:
5 + 3x2 + -30x4 = 0

Solving
5 + 3x2 + -30x4 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-30 the coefficient of the squared term: 

Divide each side by '-30'.
-0.1666666667 + -0.1x2 + x4 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + -0.1x2 + 0.1666666667 + x4 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + -0.1x2 + x4 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + -0.1x2 + x4 = 0 + 0.1666666667
-0.1x2 + x4 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
-0.1x2 + x4 = 0.1666666667

The x term is -0.1x2.  Take half its coefficient (-0.05).
Square it (0.0025) and add it to both sides.

Add '0.0025' to each side of the equation.
-0.1x2 + 0.0025 + x4 = 0.1666666667 + 0.0025

Reorder the terms:
0.0025 + -0.1x2 + x4 = 0.1666666667 + 0.0025

Combine like terms: 0.1666666667 + 0.0025 = 0.1691666667
0.0025 + -0.1x2 + x4 = 0.1691666667

Factor a perfect square on the left side:
(x2 + -0.05)(x2 + -0.05) = 0.1691666667

Calculate the square root of the right side: 0.411298756

Break this problem into two subproblems by setting 
(x2 + -0.05) equal to 0.411298756 and -0.411298756.


Subproblem 1
x2 + -0.05 = 0.411298756

Simplifying
x2 + -0.05 = 0.411298756

Reorder the terms:
-0.05 + x2 = 0.411298756

Solving
-0.05 + x2 = 0.411298756

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.05' to each side of the equation.
-0.05 + 0.05 + x2 = 0.411298756 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + x2 = 0.411298756 + 0.05
x2 = 0.411298756 + 0.05

Combine like terms: 0.411298756 + 0.05 = 0.461298756
x2 = 0.461298756

Simplifying
x2 = 0.461298756

Take the square root of each side:
x = {-0.679189779, 0.679189779}


Subproblem 2
x2 + -0.05 = -0.411298756

Simplifying
x2 + -0.05 = -0.411298756

Reorder the terms:
-0.05 + x2 = -0.411298756

Solving
-0.05 + x2 = -0.411298756

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.05' to each side of the equation.
-0.05 + 0.05 + x2 = -0.411298756 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + x2 = -0.411298756 + 0.05
x2 = -0.411298756 + 0.05

Combine like terms: -0.411298756 + 0.05 = -0.361298756
x2 = -0.361298756

Simplifying
x2 = -0.361298756

Reorder the terms:
0.361298756 + x2 = -0.361298756 + 0.361298756

Combine like terms: -0.361298756 + 0.361298756 = 0.000000000
0.361298756 + x2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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